Overview

Previous Studies

There exist 17 studies that have investigated the growth forms of Acropora cervicornis at the genotype level which have been incorporated into our database. These studies began with Diego Lirman who analyzed genotype-specific differences in annual proportionate growth (termed productivity in Lirman et al. 2014) across genotypes within Diego’s Biscayne National Park nurseries and his work in the Dominican Republic. Katie Lohr built upon this and analyzed 10 genotypes for differences in total linear extension and calcification rate over a 13 month study of CRF genotypes (Lohr and Patterson 2017). At the same time, Ford Drury analyzed the genotype niches in a genotype by environment study (Dury, Manzello, Lirman 2017). Other studies did not solely focus on differences among genotypes but their data analyzing growth under OA, temperature stress, or a combination of the two shed light on genotype-specific patterns. There has consistently been genotypic patterns of growth throughout all of these studies. Through the connection of each individual dataset, we can elucidate new, overarching genotype-specific patterns of growth. Below is a table summarizing the aforementioned and complementary studies that have analyzed growth of genotyped A. cervicornis. The remaining tables delve into the combined data of all these studies to begin to draw patterns.

Traits Table

Table 1: Summary statistics for each unqiue trait, unit, and method combination.
trait unit method mean sd min max n datasets genotypes
6-month colony volumetric growth proportionate growth 3D photogrammetry 2.5333658 4.5160081 0.0377524 60.281553 293 3 17
6-month interstitial space growth proportionate growth 3D photogrammetry 6.3103033 5.5360624 0.0692467 35.728773 135 1 10
6-month linear growth proportionate growth ruler 1.6449644 1.4264161 0.0133041 16.524444 2686 10 120
annual colony volumetric growth annual proportionate growth 3D photogrammetry 6.5244687 8.1461205 0.3835854 63.974185 170 3 18
annual interstitial space growth annual proportionate growth 3D photogrammetry 22.6691608 23.9115484 1.4555964 216.829571 123 1 10
annual linear growth annual proportionate growth ruler 6.6611193 5.8815492 0.0405556 59.211111 1583 9 81
colony volumetric SGR % change day^-1 3D photogrammetry 0.5092050 0.1972331 0.0883920 1.376506 317 4 23
daily calcification mg day^-1 buoyant weight 71.5996332 96.9861159 3.9540230 497.308997 266 5 32
dark calcification µmol cm^-2 h^-1 alkalinity anomaly 0.6967946 0.2713945 0.0180000 1.594000 56 1 12
interstitial space SGR % change day^-1 3D photogrammetry 0.7736615 0.2390515 0.2423776 1.520514 136 1 10
light calcification µmol cm^-2 h^-1 alkalinity anomaly 0.8475254 0.2766803 0.3110000 1.594000 59 1 12
mass normalized daily calcification mg day^-1 g^-1 buoyant weight 27.2406909 41.4262869 0.3450656 191.199153 244 4 27
SA normalized daily calcification mg day^-1 cm^-2 buoyant weight 1.2370585 0.3665081 0.5407155 2.884992 105 2 13
specific growth rate % change day^-1 ruler 0.5105088 0.2186303 0.0062386 1.597730 2867 11 122
  • Note: Proportionate growth indicates multiplicative growth over the time scale. If a coral was 10cm and it’s 6-month linear growth is 2, it will have grown 20cm in the 6-months and it’s new size is 30cm.

Connecting Across Datasets

We can then look at the mean value of each metric for each genotype. The columns have been ordered by their amount of data completeness. Columns to the left of the vertical line describe linear extension, while columns to the right of the line describe total calcification. Linear extension includes TLE and volumetric methods for a total of 9 metrics, and calcification metrics include buoyant weight and total alkalinity anomaly methodologies for a total of 5 metrics. The large amounts of missing data will force us to impute many data points.
genotype specific growth rate 6-month linear growth annual linear growth colony volumetric SGR annual colony volumetric growth 6-month colony volumetric growth 6-month interstitial space growth annual interstitial space growth interstitial space SGR daily calcification mass normalized daily calcification SA normalized daily calcification dark calcification light calcification
ML41 0.40 1.32 3.96 0.45 4.09 2.31 6.34 16.72 0.80 22.02 1.85 1.13 0.91 0.82
ML7 0.36 0.99 3.48 0.53 7.25 1.88 6.93 32.14 0.86 34.82 2.51 1.25 0.74 0.88
ML62 0.56 2.10 4.88 0.49 6.67 1.73 7.52 30.94 0.83 9.57 1.90 0.98 0.48 0.84
ML50 0.51 1.86 5.62 0.43 6.05 1.55 6.68 30.46 0.74 10.98 2.34 1.25 0.84 0.73
ML31 0.43 1.86 4.40 0.35 2.73 1.54 6.41 16.42 0.71 20.17 2.05 1.13 0.92 0.87
ML3 0.43 1.70 4.55 0.44 5.13 1.51 5.77 19.12 0.71 9.66 2.02 1.09 0.75 0.71
ML44 0.43 1.15 4.51 0.50 6.35 1.31 4.37 17.44 0.70 21.41 2.10 1.20 0.65 0.99
ML1 0.45 1.50 3.80 0.43 4.63 1.30 3.98 17.74 0.76 15.87 1.32 1.36 0.64 0.67
ML13 0.46 1.29 3.42 0.35 2.94 1.13 6.73 19.49 0.78 7.12 1.54 0.92 0.65 0.87
ML36 0.39 0.95 3.66 0.49 5.82 1.70 7.94 23.95 0.85 - - - - -
M6 0.57 1.72 - 0.54 11.98 5.30 - - - 12.77 0.89 - - -
U41 0.70 5.52 13.29 0.54 5.30 - - - - 159.83 65.67 - - -
K3 0.72 5.08 14.59 0.34 2.39 - - - - 189.47 84.94 - - -
K2 0.68 4.51 15.98 0.32 2.54 - - - - 199.95 84.65 - - -
U77 0.65 4.01 10.08 0.62 6.98 - - - - 150.69 54.90 - - -
U44 0.63 3.64 11.19 0.45 4.26 - - - - 123.64 47.16 - - -
ML34 0.58 2.12 - - - - - - - 12.38 2.10 1.07 0.57 0.85
Marker 9 0.56 1.67 8.89 0.53 - 1.80 - - - - - - - -
U47 0.80 4.70 18.24 - - - - - - 120.05 52.37 - - -
U73 0.82 4.61 19.55 - - - - - - 137.15 46.89 - - -
U78 0.79 4.10 16.52 - - - - - - 146.81 47.16 - - -
K1 0.79 3.93 15.47 - - - - - - 90.84 34.87 - - -
K25 0.63 3.02 9.95 - - - - - - 72.80 23.20 - - -
ML20 0.44 1.21 - - - - - - - 10.31 1.13 1.31 - -
ML63 - - - - - - - - - 10.97 2.25 1.24 0.38 0.92
ML47 - - - - - - - - - 10.96 2.20 1.25 0.84 1.01
BC-G 0.33 0.76 - 0.61 - 2.52 - - - - - - - -
Stagreef 0.44 1.13 - 0.63 - 2.49 - - - - - - - -
Sunny Isles-F 0.40 1.00 - 0.56 - 2.02 - - - - - - - -
BC-H 0.56 1.61 - 0.50 - 1.58 - - - - - - - -
ML5 0.59 2.82 5.50 - - - - - - 63.40 - - - -
ML56 0.48 2.18 3.38 - - - - - - 22.90 - - - -
ML54 0.48 1.87 3.99 - - - - - - 34.10 - - - -
U25 0.26 - 1.63 0.61 5.38 - - - - - - - - -
FM20 - - - 0.59 16.16 8.02 - - - - - - - -
B 0.78 3.61 18.89 - - - - - - - - - - -
DR-A 0.49 2.45 5.40 - - - - - - - - - - -
THIN 0.55 2.19 6.78 - - - - - - - - - - -
Acerv 1 (A-AC) 0.59 2.00 7.89 - - - - - - - - - - -
ELK 0.50 1.74 5.36 - - - - - - - - - - -
G1 0.49 1.66 5.27 - - - - - - - - - - -
Struggle Bus 0.52 1.66 9.27 - - - - - - - - - - -
Acerv 3 (C-AC) 0.55 1.63 7.82 - - - - - - - - - - -
Acerv 2 (B-AC) 0.54 1.61 5.26 - - - - - - - - - - -
Site 406 0.52 1.61 8.05 - - - - - - - - - - -
G16 0.55 1.58 6.75 - - - - - - - - - - -
TT (Thicket 3) 0.48 1.53 3.25 - - - - - - - - - - -
FM12 0.38 1.50 1.33 - - - - - - - - - - -
Acerv 5 (E-AC) 0.46 1.46 7.24 - - - - - - - - - - -
G17 0.54 1.43 6.39 - - - - - - - - - - -
ML4 0.42 1.38 3.82 - - - - - - - - - - -
U24 0.42 1.33 3.84 - - - - - - - - - - -
Steph’s 0.52 1.33 10.34 - - - - - - - - - - -
Trans 2 0.52 1.27 7.51 - - - - - - - - - - -
THICK 0.38 1.27 2.87 - - - - - - - - - - -
Grounding 0.45 1.26 5.07 - - - - - - - - - - -
G11 0.42 1.26 3.78 - - - - - - - - - - -
Dom’s Reef 0.57 1.25 9.31 - - - - - - - - - - -
G6 0.39 1.15 3.82 - - - - - - - - - - -
Cooper’s 0.45 1.12 4.53 - - - - - - - - - - -
Inshore 0.40 1.09 4.08 - - - - - - - - - - -
FM5 0.26 1.08 3.10 - - - - - - - - - - -
Trav’s Reef 0.54 1.05 7.62 - - - - - - - - - - -
FM7 0.25 1.05 1.97 - - - - - - - - - - -
Britt’s Reef 0.47 1.01 9.59 - - - - - - - - - - -
FM18 0.30 0.91 2.08 - - - - - - - - - - -
FM13 0.25 0.90 1.78 - - - - - - - - - - -
FM1 0.24 0.90 4.37 - - - - - - - - - - -
FM10 0.39 0.89 2.48 - - - - - - - - - - -
Almost Done 0.41 0.87 6.22 - - - - - - - - - - -
Ford’s Reef 0.52 0.86 10.78 - - - - - - - - - - -
G15 0.47 0.86 5.03 - - - - - - - - - - -
G2 0.42 0.85 4.38 - - - - - - - - - - -
Acerv 4 (D-AC) 0.54 0.84 7.05 - - - - - - - - - - -
MUTANT182 0.42 0.83 3.83 - - - - - - - - - - -
Alina-B 0.53 0.82 6.81 - - - - - - - - - - -
Alina-A 0.59 0.70 7.81 - - - - - - - - - - -
Big Bertha 0.45 0.70 5.20 - - - - - - - - - - -
Fowey 0.47 0.60 6.29 - - - - - - - - - - -
Navassa 0.33 0.59 2.34 - - - - - - - - - - -
B/B 0.38 0.58 2.94 - - - - - - - - - - -
Trans 1 0.38 0.56 4.82 - - - - - - - - - - -
FM9 0.35 0.54 2.27 - - - - - - - - - - -
G18 0.24 0.51 1.64 - - - - - - - - - - -
North Midchannel-A 0.68 0.49 9.07 - - - - - - - - - - -
W/Y 0.21 0.40 2.47 - - - - - - - - - - -
W/G 0.31 0.34 7.10 - - - - - - - - - - -
W/B 0.29 0.30 3.51 - - - - - - - - - - -
Sunny Isles-A 0.90 4.50 - - - - - - - - - - - -
Stag-B 0.86 4.05 - - - - - - - - - - - -
MB-C 0.86 3.90 - - - - - - - - - - - -
MB-A 0.85 3.83 - - - - - - - - - - - -
BC-8A 0.83 3.79 - - - - - - - - - - - -
Cheetos-C 0.83 3.71 - - - - - - - - - - - -
MB-B 0.78 3.39 - - - - - - - - - - - -
Sunny Isles-C 0.78 3.38 - - - - - - - - - - - -
Stag-A 0.78 3.31 - - - - - - - - - - - -
BC-8B 0.79 3.30 - - - - - - - - - - - -
Cheetos-D 0.74 3.15 - - - - - - - - - - - -
BC-11 0.73 3.01 - - - - - - - - - - - -
Tuna Jelly-B 0.79 2.95 - - - - - - - - - - - -
MB-D 0.73 2.88 - - - - - - - - - - - -
Sunny Isles-B 0.71 2.82 - - - - - - - - - - - -
Sunny Isles-D 0.68 2.73 - - - - - - - - - - - -
FM17 0.65 2.50 - - - - - - - - - - - -
Tuna Jelly-A 0.71 2.46 - - - - - - - - - - - -
Yung’s-B 0.66 2.45 - - - - - - - - - - - -
Kelsey-1 0.63 2.38 - - - - - - - - - - - -
Yung’s-A 0.62 2.36 - - - - - - - - - - - -
Kelsey-2 0.63 2.33 - - - - - - - - - - - -
BC-1 0.61 2.26 - - - - - - - - - - - -
Cheetos-A 0.61 2.25 - - - - - - - - - - - -
ML48 0.63 2.24 - - - - - - - - - - - -
Site 211 0.56 1.64 - - - - - - - - - - - -
FM15 0.26 1.62 - - - - - - - - - - - -
MB 0.52 1.61 - - - - - - - - - - - -
Govt Cut 0.55 1.58 - - - - - - - - - - - -
Cheetos-B 0.42 1.37 - - - - - - - - - - - -
ML14 0.50 1.35 - - - - - - - - - - - -
FM16 0.32 1.34 - - - - - - - - - - - -
Jons 0.45 1.26 - - - - - - - - - - - -
FM3 0.22 0.80 - - - - - - - - - - - -
FM11 0.22 0.80 - - - - - - - - - - - -
FM19 0.24 0.47 - - - - - - - - - - - -
ML38 - - 3.66 - - - - - - 43.80 - - - -
ML43 - - 2.59 - - - - - - 29.97 - - - -
ML11 0.25 - 1.01 - - - - - - - - - - -
M10 - - - - - - - - - 34.88 2.23 - - -
B8 - - - - - - - - - 22.40 1.32 - - -
M1 - - - - - - - - - 10.38 0.58 - - -

Standardizing Scores

Because each of these metrics describe a different component of coral growth and are measured on different scales, they cannot be directly aggregated. Instead, we must first calculate standardized scores for each metric prior to aligning disparate measurements. I chose to standardize by calculating z-scores where the difference of each value and the column mean is divided by the column’s standard deviation. Thus, the column mean is now 0 and the standard deviation is 1. Each resulting value indicates the amount of standard deviations about the mean for that metric.

I then group together all linear extension metrics to calculate a genotype’s average standard deviation about the mean and impute this value for all missing linear extension metrics. I do the same for calcification metrics. If no calcification or no linear extension metrics exist for a particular genotype, then 0’s are imputed for all calcification or no linear extension metrics, which signifies average performance.

The table below shows the resulting standardized data with scores in black indicating calculated z-scores, scores in blue indicating imputed z-scores based on the other linear extension or calcification scores, and scores in red indicating imputed scores of 0 if no linear extension or calcification data was available.
genotype specific growth rate 6-month linear growth annual linear growth colony volumetric SGR annual colony volumetric growth 6-month colony volumetric growth 6-month interstitial space growth annual interstitial space growth interstitial space SGR daily calcification mass normalized daily calcification SA normalized daily calcification dark calcification light calcification
ML41 -0.73 -0.49 -0.57 -0.39 -0.54 -0.01 0.06 -0.89 0.45 -0.6 -0.68 -0.33 1.26 -0.22
ML7 -0.95 -0.77 -0.68 0.43 0.39 -0.26 0.53 1.51 1.41 -0.39 -0.66 0.61 0.25 0.3
ML62 0.24 0.17 -0.35 -0.01 0.22 -0.35 0.99 1.33 0.92 -0.8 -0.68 -1.42 -1.27 -0.06
ML50 -0.06 -0.02 -0.17 -0.7 0.04 -0.45 0.33 1.25 -0.59 -0.78 -0.67 0.65 0.86 -1.11
ML31 -0.52 -0.02 -0.46 -1.53 -0.94 -0.46 0.11 -0.94 -1.1 -0.63 -0.68 -0.31 1.31 0.19
ML3 -0.53 -0.16 -0.43 -0.6 -0.23 -0.47 -0.39 -0.52 -1.07 -0.8 -0.68 -0.63 0.28 -1.33
ML44 -0.53 -0.63 -0.43 0.07 0.12 -0.59 -1.51 -0.78 -1.22 -0.61 -0.68 0.27 -0.28 1.41
ML1 -0.45 -0.33 -0.6 -0.66 -0.38 -0.59 -1.81 -0.74 -0.23 -0.7 -0.7 1.51 -0.35 -1.69
ML13 -0.34 -0.51 -0.69 -1.48 -0.88 -0.69 0.37 -0.46 0.13 -0.84 -0.7 -1.93 -0.28 0.25
ML36 -0.76 -0.79 -0.64 -0.01 -0.03 -0.36 1.33 0.24 1.3 0 0 0 0 0
M6 0.27 -0.15 0.82 0.48 1.78 1.7 0.82 0.82 0.82 -0.75 -0.72 -0.73 -0.73 -0.73
U41 1.05 3.07 1.64 0.56 -0.18 1.23 1.23 1.23 1.23 1.68 1.57 1.63 1.63 1.63
K3 1.18 2.7 1.95 -1.66 -1.04 0.63 0.63 0.63 0.63 2.17 2.25 2.21 2.21 2.21
K2 0.94 2.21 2.28 -1.78 -0.99 0.53 0.53 0.53 0.53 2.34 2.24 2.29 2.29 2.29
U77 0.74 1.79 0.88 1.34 0.31 1.01 1.01 1.01 1.01 1.53 1.19 1.36 1.36 1.36
U44 0.61 1.48 1.15 -0.47 -0.49 0.45 0.45 0.45 0.45 1.08 0.92 1 1 1
ML34 0.35 0.2 0.28 0.28 0.28 0.28 0.28 0.28 0.28 -0.76 -0.68 -0.73 -0.75 0.03
Marker 9 0.2 -0.19 0.6 0.45 0.15 -0.31 0.15 0.15 0.15 0 0 0 0 0
U47 1.66 2.37 2.82 2.28 2.28 2.28 2.28 2.28 2.28 1.02 1.1 1.06 1.06 1.06
U73 1.74 2.3 3.13 2.39 2.39 2.39 2.39 2.39 2.39 1.3 0.91 1.11 1.11 1.11
U78 1.55 1.87 2.41 1.94 1.94 1.94 1.94 1.94 1.94 1.46 0.92 1.19 1.19 1.19
K1 1.56 1.72 2.16 1.81 1.81 1.81 1.81 1.81 1.81 0.54 0.48 0.51 0.51 0.51
K25 0.63 0.96 0.85 0.81 0.81 0.81 0.81 0.81 0.81 0.24 0.07 0.16 0.16 0.16
ML20 -0.51 -0.58 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.79 -0.71 1.12 -0.13 -0.13
ML63 0 0 0 0 0 0 0 0 0 -0.78 -0.67 0.56 -1.9 0.66
ML47 0 0 0 0 0 0 0 0 0 -0.78 -0.67 0.63 0.86 1.57
BC-G -1.11 -0.96 -0.17 1.29 -0.17 0.11 -0.17 -0.17 -0.17 0 0 0 0 0
Stagreef -0.5 -0.65 0.11 1.5 0.11 0.09 0.11 0.11 0.11 0 0 0 0 0
Sunny Isles-F -0.75 -0.76 -0.24 0.73 -0.24 -0.18 -0.24 -0.24 -0.24 0 0 0 0 0
BC-H 0.2 -0.24 -0.09 0.12 -0.09 -0.43 -0.09 -0.09 -0.09 0 0 0 0 0
ML5 0.38 0.78 -0.2 0.32 0.32 0.32 0.32 0.32 0.32 0.09 0.09 0.09 0.09 0.09
ML56 -0.24 0.24 -0.7 -0.23 -0.23 -0.23 -0.23 -0.23 -0.23 -0.58 -0.58 -0.58 -0.58 -0.58
ML54 -0.25 -0.02 -0.56 -0.27 -0.27 -0.27 -0.27 -0.27 -0.27 -0.4 -0.4 -0.4 -0.4 -0.4
U25 -1.53 -0.39 -1.12 1.23 -0.16 -0.39 -0.39 -0.39 -0.39 0 0 0 0 0
FM20 2.45 2.45 2.45 1.09 3 3.26 2.45 2.45 2.45 0 0 0 0 0
B 1.51 1.46 2.97 1.98 1.98 1.98 1.98 1.98 1.98 0 0 0 0 0
DR-A -0.17 0.47 -0.22 0.03 0.03 0.03 0.03 0.03 0.03 0 0 0 0 0
THIN 0.19 0.25 0.1 0.18 0.18 0.18 0.18 0.18 0.18 0 0 0 0 0
Acerv 1 (A-AC) 0.41 0.09 0.36 0.29 0.29 0.29 0.29 0.29 0.29 0 0 0 0 0
ELK -0.12 -0.13 -0.23 -0.16 -0.16 -0.16 -0.16 -0.16 -0.16 0 0 0 0 0
G1 -0.16 -0.2 -0.26 -0.21 -0.21 -0.21 -0.21 -0.21 -0.21 0 0 0 0 0
Struggle Bus -0.01 -0.2 0.69 0.16 0.16 0.16 0.16 0.16 0.16 0 0 0 0 0
Acerv 3 (C-AC) 0.18 -0.22 0.35 0.1 0.1 0.1 0.1 0.1 0.1 0 0 0 0 0
Acerv 2 (B-AC) 0.08 -0.24 -0.26 -0.14 -0.14 -0.14 -0.14 -0.14 -0.14 0 0 0 0 0
Site 406 -0.03 -0.24 0.4 0.04 0.04 0.04 0.04 0.04 0.04 0 0 0 0 0
G16 0.17 -0.26 0.09 0 0 0 0 0 0 0 0 0 0 0
TT (Thicket 3) -0.25 -0.3 -0.73 -0.43 -0.43 -0.43 -0.43 -0.43 -0.43 0 0 0 0 0
FM12 -0.83 -0.33 -1.19 -0.78 -0.78 -0.78 -0.78 -0.78 -0.78 0 0 0 0 0
Acerv 5 (E-AC) -0.38 -0.37 0.21 -0.18 -0.18 -0.18 -0.18 -0.18 -0.18 0 0 0 0 0
G17 0.1 -0.39 0.01 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0 0 0 0 0
ML4 -0.62 -0.44 -0.6 -0.55 -0.55 -0.55 -0.55 -0.55 -0.55 0 0 0 0 0
U24 -0.62 -0.47 -0.59 -0.56 -0.56 -0.56 -0.56 -0.56 -0.56 0 0 0 0 0
Steph’s 0 -0.47 0.94 0.16 0.16 0.16 0.16 0.16 0.16 0 0 0 0 0
Trans 2 0.01 -0.53 0.28 -0.08 -0.08 -0.08 -0.08 -0.08 -0.08 0 0 0 0 0
THICK -0.83 -0.53 -0.82 -0.73 -0.73 -0.73 -0.73 -0.73 -0.73 0 0 0 0 0
Grounding -0.43 -0.53 -0.3 -0.42 -0.42 -0.42 -0.42 -0.42 -0.42 0 0 0 0 0
G11 -0.63 -0.54 -0.61 -0.59 -0.59 -0.59 -0.59 -0.59 -0.59 0 0 0 0 0
Dom’s Reef 0.3 -0.54 0.7 0.15 0.15 0.15 0.15 0.15 0.15 0 0 0 0 0
G6 -0.76 -0.63 -0.6 -0.66 -0.66 -0.66 -0.66 -0.66 -0.66 0 0 0 0 0
Cooper’s -0.42 -0.66 -0.43 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 0 0 0 0 0
Inshore -0.7 -0.68 -0.54 -0.64 -0.64 -0.64 -0.64 -0.64 -0.64 0 0 0 0 0
FM5 -1.57 -0.69 -0.77 -1.01 -1.01 -1.01 -1.01 -1.01 -1.01 0 0 0 0 0
Trav’s Reef 0.1 -0.71 0.3 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0 0 0 0 0
FM7 -1.6 -0.71 -1.04 -1.12 -1.12 -1.12 -1.12 -1.12 -1.12 0 0 0 0 0
Britt’s Reef -0.32 -0.75 0.77 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0 0 0 0 0
FM18 -1.33 -0.83 -1.01 -1.06 -1.06 -1.06 -1.06 -1.06 -1.06 0 0 0 0 0
FM13 -1.63 -0.84 -1.08 -1.18 -1.18 -1.18 -1.18 -1.18 -1.18 0 0 0 0 0
FM1 -1.65 -0.84 -0.47 -0.99 -0.99 -0.99 -0.99 -0.99 -0.99 0 0 0 0 0
FM10 -0.76 -0.85 -0.91 -0.84 -0.84 -0.84 -0.84 -0.84 -0.84 0 0 0 0 0
Almost Done -0.68 -0.86 -0.03 -0.52 -0.52 -0.52 -0.52 -0.52 -0.52 0 0 0 0 0
Ford’s Reef -0.03 -0.87 1.05 0.05 0.05 0.05 0.05 0.05 0.05 0 0 0 0 0
G15 -0.3 -0.87 -0.31 -0.49 -0.49 -0.49 -0.49 -0.49 -0.49 0 0 0 0 0
G2 -0.58 -0.88 -0.47 -0.64 -0.64 -0.64 -0.64 -0.64 -0.64 0 0 0 0 0
Acerv 4 (D-AC) 0.11 -0.89 0.17 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 0 0 0 0 0
MUTANT182 -0.6 -0.9 -0.6 -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 0 0 0 0 0
Alina-B 0.03 -0.91 0.11 -0.26 -0.26 -0.26 -0.26 -0.26 -0.26 0 0 0 0 0
Alina-A 0.38 -1.01 0.35 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0 0 0 0 0
Big Bertha -0.43 -1.01 -0.27 -0.57 -0.57 -0.57 -0.57 -0.57 -0.57 0 0 0 0 0
Fowey -0.31 -1.1 -0.01 -0.47 -0.47 -0.47 -0.47 -0.47 -0.47 0 0 0 0 0
Navassa -1.16 -1.1 -0.95 -1.07 -1.07 -1.07 -1.07 -1.07 -1.07 0 0 0 0 0
B/B -0.85 -1.11 -0.81 -0.92 -0.92 -0.92 -0.92 -0.92 -0.92 0 0 0 0 0
Trans 1 -0.85 -1.13 -0.36 -0.78 -0.78 -0.78 -0.78 -0.78 -0.78 0 0 0 0 0
FM9 -1.04 -1.14 -0.97 -1.05 -1.05 -1.05 -1.05 -1.05 -1.05 0 0 0 0 0
G18 -1.65 -1.17 -1.12 -1.31 -1.31 -1.31 -1.31 -1.31 -1.31 0 0 0 0 0
North Midchannel-A 0.92 -1.19 0.64 0.13 0.13 0.13 0.13 0.13 0.13 0 0 0 0 0
W/Y -1.85 -1.27 -0.92 -1.34 -1.34 -1.34 -1.34 -1.34 -1.34 0 0 0 0 0
W/G -1.26 -1.31 0.18 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 0 0 0 0 0
W/B -1.4 -1.35 -0.67 -1.14 -1.14 -1.14 -1.14 -1.14 -1.14 0 0 0 0 0
Sunny Isles-A 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 0 0 0 0 0
Stag-B 1.97 1.83 1.9 1.9 1.9 1.9 1.9 1.9 1.9 0 0 0 0 0
MB-C 1.97 1.7 1.84 1.84 1.84 1.84 1.84 1.84 1.84 0 0 0 0 0
MB-A 1.91 1.64 1.78 1.78 1.78 1.78 1.78 1.78 1.78 0 0 0 0 0
BC-8A 1.81 1.61 1.71 1.71 1.71 1.71 1.71 1.71 1.71 0 0 0 0 0
Cheetos-C 1.81 1.54 1.68 1.68 1.68 1.68 1.68 1.68 1.68 0 0 0 0 0
MB-B 1.5 1.26 1.38 1.38 1.38 1.38 1.38 1.38 1.38 0 0 0 0 0
Sunny Isles-C 1.5 1.26 1.38 1.38 1.38 1.38 1.38 1.38 1.38 0 0 0 0 0
Stag-A 1.49 1.2 1.34 1.34 1.34 1.34 1.34 1.34 1.34 0 0 0 0 0
BC-8B 1.55 1.19 1.37 1.37 1.37 1.37 1.37 1.37 1.37 0 0 0 0 0
Cheetos-D 1.26 1.07 1.16 1.16 1.16 1.16 1.16 1.16 1.16 0 0 0 0 0
BC-11 1.24 0.95 1.09 1.09 1.09 1.09 1.09 1.09 1.09 0 0 0 0 0
Tuna Jelly-B 1.56 0.9 1.23 1.23 1.23 1.23 1.23 1.23 1.23 0 0 0 0 0
MB-D 1.22 0.83 1.03 1.03 1.03 1.03 1.03 1.03 1.03 0 0 0 0 0
Sunny Isles-B 1.13 0.79 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0 0 0 0 0
Sunny Isles-D 0.93 0.71 0.82 0.82 0.82 0.82 0.82 0.82 0.82 0 0 0 0 0
FM17 0.73 0.52 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0 0 0 0 0
Tuna Jelly-A 1.08 0.48 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0 0 0 0 0
Yung’s-B 0.8 0.47 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0 0 0 0 0
Kelsey-1 0.61 0.41 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0 0 0 0 0
Yung’s-A 0.56 0.39 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0 0 0 0 0
Kelsey-2 0.62 0.37 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0 0 0 0 0
BC-1 0.52 0.31 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0 0 0 0 0
Cheetos-A 0.49 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0 0 0 0 0
ML48 0.64 0.29 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0 0 0 0 0
Site 211 0.24 -0.21 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0 0 0 0 0
FM15 -1.56 -0.23 -0.9 -0.9 -0.9 -0.9 -0.9 -0.9 -0.9 0 0 0 0 0
MB -0.04 -0.24 -0.14 -0.14 -0.14 -0.14 -0.14 -0.14 -0.14 0 0 0 0 0
Govt Cut 0.17 -0.27 -0.05 -0.05 -0.05 -0.05 -0.05 -0.05 -0.05 0 0 0 0 0
Cheetos-B -0.59 -0.44 -0.52 -0.52 -0.52 -0.52 -0.52 -0.52 -0.52 0 0 0 0 0
ML14 -0.14 -0.46 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 0 0 0 0 0
FM16 -1.2 -0.47 -0.84 -0.84 -0.84 -0.84 -0.84 -0.84 -0.84 0 0 0 0 0
Jons -0.43 -0.53 -0.48 -0.48 -0.48 -0.48 -0.48 -0.48 -0.48 0 0 0 0 0
FM3 -1.77 -0.92 -1.35 -1.35 -1.35 -1.35 -1.35 -1.35 -1.35 0 0 0 0 0
FM11 -1.76 -0.93 -1.35 -1.35 -1.35 -1.35 -1.35 -1.35 -1.35 0 0 0 0 0
FM19 -1.64 -1.2 -1.42 -1.42 -1.42 -1.42 -1.42 -1.42 -1.42 0 0 0 0 0
ML38 -0.64 -0.64 -0.64 -0.64 -0.64 -0.64 -0.64 -0.64 -0.64 -0.24 -0.24 -0.24 -0.24 -0.24
ML43 -0.89 -0.89 -0.89 -0.89 -0.89 -0.89 -0.89 -0.89 -0.89 -0.47 -0.47 -0.47 -0.47 -0.47
ML11 -1.6 -1.43 -1.26 -1.43 -1.43 -1.43 -1.43 -1.43 -1.43 0 0 0 0 0
M10 0 0 0 0 0 0 0 0 0 -0.39 -0.67 -0.53 -0.53 -0.53
B8 0 0 0 0 0 0 0 0 0 -0.59 -0.7 -0.65 -0.65 -0.65
M1 0 0 0 0 0 0 0 0 0 -0.79 -0.73 -0.76 -0.76 -0.76
  • Note: Some genotypes (ML38, ML43, Sunny Isles-A) may have an entire row highlighted in blue suggesting all data is imputed. However, this is an artifact of my conditional formatting and not accurate. One or two of the actual, calculated z-scores is the same as the row mean and is being incorrectly colored. Decided not to spend unnecessary time figuring this out and made this quick note instead.

Composite Growth Index

Now that we have standardized scores for 14 different metrics, we can compare and align metrics into a single, composite index to understand relative genotype performance.

Methods

First, I group the growth metrics into their two large determinants of linear extension and calcification and calculate the mean standardized score for each of these determinants of growth.

Then, I individually weight the linear extension and calcification scores. The derivation of the two distinct weights is explained below. The two weights add to 1.

Finally, the two weighted values are added together for a finalized score. For genotypes that only have linear extension data or calcification data, the resulting score is just the weighed linear extension or calcification score. Since average performance has a score of 0 and the two determinants of growth are independently weighed with the sum of the weights equaling 1, the finalized score should best encapsulate true growth rates and permit ranking of relative genotype performance.

This process assumes there is no genotype-effect on density, which is supported by Kuffner et al. (2017) who demonstrated for this species a genotype-specific calcification rate but a plastic density based on its nursery grow out structure.

Derivation of Weights

Weights were determined by characteristic growth of the species, a common practice in calicification budgets of coral reefs. Briefly, calcification is the product of densification and linear extension, and is the total metric we are trying to describe. We have metrics that measure calcification through buoyant weight or total alkalinity anomaly measurements. We also have various determinations of linear extension as it is a common metric captured in the field, but this rapid growth is biased by the quick growing branch tips which is only about 24.6% of the coral’s volume, with the other 75.4% of the coral growing at a rate 10% of the branch tips (data aggregated by Perry Reef Budget, see citations within).

The formula for calculating the gross calcification of a branching A. cervicornis is: \[ G = (l \times c_a \times P \times \rho) + ((l-c_a \times l)\times 0.1 \times P \times \rho) \] where

  1. \(G\) = total gross calcification of the two terms \(g/cm^2/yr\) or \(g/cm^2/day\)
  2. \(l\) = the initial length of the coral in cm
  3. \(c_a\) = proportion of colony fast-growing axial tips (0.246)
  4. \(P\) = relative linear extension of the coral \(yr^{-1}\) or \(day^{-1}\) (termed productivity in Lirman et al. 2014)
  5. \(\rho\) = the average density of the coral in \(g/cm^3\)

As you can see, the first term is for the fast linear extension of the branches, and the second term is for the growth of the remaining portion of the colony, growing at a rate 10% of the branch tips. We can combine the constant terms and simplify the equation to:

\[ G = (0.246 \times Q) + (0.754 \times 0.1 \times Q) \] where Q is the terms \(l \times P \times \rho\) combined. Thus the ratio of linear extension to gross calcification is: \[ \frac{\text{LE}}{ G} = \frac{0.246}{0.0754 + 0.246} = \frac{0.246}{0.3214} = 0.7654 \]

Therefore, by measuring linear extension you are describing only 76.54% of the colony growth, while if you measure the calcification, you are describing 100% of the colony’s growth. Our goal is to have these percentages converted to weights which add to 1 to provide simple understanding and calculating of weighted arithmetic means.

\[ 0.7654x + x = 1 \rightarrow 1.7654x =1 \rightarrow x = 1/1.7654 \approx 0.57 \]

Finally, our weighting for calcification measurements take the weight of 0.57 and linear extension measurements take the weight of 1-0.57 or 0.43.

Weight Breakdown

Robustness Testing

Lets Graph It Out

genotype score rank tercile
U73 1.658 1 1
U47 1.587 2 1
K2 1.536 3 1
K3 1.530 4 1
U78 1.515 5 1
U41 1.455 6 1
U77 1.210 7 1
K1 1.072 8 1
FM20 1.054 9 1
Sunny Isles-A 0.946 10 1
B 0.851 11 1
Stag-B 0.817 12 1
MB-C 0.790 13 1
U44 0.765 14 1
MB-A 0.764 15 1
BC-8A 0.736 16 1
Cheetos-C 0.721 17 1
MB-B 0.594 18 1
Sunny Isles-C 0.593 19 1
BC-8B 0.588 20 1
Stag-A 0.578 21 1
Tuna Jelly-B 0.528 22 1
Cheetos-D 0.499 23 1
BC-11 0.471 24 1
MB-D 0.442 25 1
K25 0.439 26 1
Sunny Isles-B 0.411 27 1
Sunny Isles-D 0.351 28 1
Tuna Jelly-A 0.336 29 1
Yung’s-B 0.273 30 1
FM17 0.267 31 1
Kelsey-1 0.219 32 1
Kelsey-2 0.212 33 1
Yung’s-A 0.206 34 1
ML48 0.200 35 1
ML5 0.187 36 1
ML47 0.184 37 1
BC-1 0.178 38 1
Cheetos-A 0.170 39 1
Acerv 1 (A-AC) 0.124 40 1
ML7 0.090 41 1
THIN 0.077 42 1
Struggle Bus 0.069 43 1
Steph’s 0.067 44 1
Dom’s Reef 0.066 45 2
Marker 9 0.065 46 2
North Midchannel-A 0.054 47 2
Stagreef 0.047 48 2
Acerv 3 (C-AC) 0.044 49 2
Ford’s Reef 0.020 50 2
Site 406 0.018 51 2
ML36 0.013 52 2
DR-A 0.012 53 2
Site 211 0.007 54 2
G16 0.000 55 2
Govt Cut -0.021 56 2
Trans 2 -0.034 57 2
BC-H -0.038 58 2
G17 -0.041 59 2
Alina-A -0.041 60 2
Britt’s Reef -0.043 61 2
Trav’s Reef -0.045 62 2
Acerv 2 (B-AC) -0.059 63 2
MB -0.060 64 2
M6 -0.067 65 2
ELK -0.069 66 2
BC-G -0.072 67 2
Acerv 5 (E-AC) -0.076 68 2
Acerv 4 (D-AC) -0.087 69 2
G1 -0.088 70 2
Sunny Isles-F -0.103 71 2
Alina-B -0.111 72 2
ML14 -0.130 73 2
ML50 -0.136 74 2
U25 -0.169 75 2
Grounding -0.180 76 2
TT (Thicket 3) -0.184 77 2
Fowey -0.203 78 2
Jons -0.208 79 2
ML34 -0.210 80 2
G15 -0.212 81 2
ML41 -0.214 82 2
Cooper’s -0.216 83 2
Cheetos-B -0.223 84 2
Almost Done -0.225 85 2
ML4 -0.238 86 2
U24 -0.241 87 2
ML63 -0.243 88 3
Big Bertha -0.245 89 3
ML44 -0.249 90 3
G11 -0.254 91 3
Inshore -0.275 92 3
G2 -0.277 93 3
G6 -0.285 94 3
ML31 -0.293 95 3
MUTANT182 -0.300 96 3
M10 -0.301 97 3
ML20 -0.307 98 3
THICK -0.313 99 3
ML62 -0.332 100 3
Trans 1 -0.335 101 3
FM12 -0.337 102 3
W/G -0.343 103 3
ML54 -0.345 104 3
FM16 -0.359 105 3
FM10 -0.362 106 3
B8 -0.369 107 3
FM15 -0.385 108 3
B/B -0.397 109 3
ML38 -0.409 110 3
FM1 -0.424 111 3
ML56 -0.432 112 3
M1 -0.433 113 3
FM5 -0.433 114 3
FM9 -0.451 115 3
FM18 -0.455 116 3
Navassa -0.460 117 3
FM7 -0.481 118 3
W/B -0.490 119 3
ML1 -0.496 120 3
FM13 -0.508 121 3
G18 -0.565 122 3
ML3 -0.571 123 3
W/Y -0.578 124 3
FM11 -0.578 125 3
FM3 -0.580 126 3
FM19 -0.611 127 3
ML13 -0.616 128 3
ML11 -0.616 129 3
ML43 -0.648 130 3

There is a cluster of the type of metric and the number of metrics (purple), which makes sense as if there are two types of metrics represented, then there is a high likelihood that both calcification and linear extension metrics are represented. However, there is no clustering of the number of metrics and the score. Finally, there is slight clustering of the type of metric and the score (black), with genotypes that have both metrics represented being on average higher than genotypes represented by linear extension or calcification metrics alone.

Statistical Tests

Comparison of the number of metrics as a function of the classified type (purple). Both denotes linear extension and calcification metrics are represented in the composite index.
contrast estimate conf.low conf.high adj.p.value
G-Both -4.985 -7.476 -2.494 0.000
LE-Both -5.430 -6.542 -4.318 0.000
LE-G -0.445 -2.790 1.901 0.895
Comparison of the composite index as a function of the number of metrics repesented.
term estimate std.error statistic p.value
(Intercept) 0.066 0.074 0.886 0.377
metrics -0.005 0.015 -0.347 0.729
Comparison of the composite index as a function of the classified type (black). Both denotes linear extension and calcification metrics are represented in the composite index.
contrast estimate conf.low conf.high adj.p.value
G-Both -0.518 -1.105 0.069 0.095
LE-Both -0.292 -0.554 -0.030 0.025
LE-G 0.226 -0.327 0.778 0.598

Analysis

We can then dive into the 9 clustered (black) genotypes which are driving this statistically significant difference (have a score >0.5 and have both metrics represented). They all happen to be CRF genotypes used by Katie Lohr in her PhD work at UF and Dan Paradis in his masters work at Auburn. This data is distinguished as only having a few data points in an Auburn lab for buoyant weight measurements while all other measurements come from the field and inshore patch reefs. Katie Lohr measured the linear extension and calcification of the corals in a CRF nursery and is the main driver of why these corals are classified as ‘Both’.

genotype datafile_name location_name
K1 Paradis2019 Auburn Lab
K1 LohrPatterson2017 CRF Tavenier Nursery
K2 LohrPatterson2017 CRF Tavenier Nursery
K2 Lohr2020 U4 Patch
K2 Lohr2020 U14 Patch
K3 LohrPatterson2017 CRF Tavenier Nursery
K3 Lohr2020 U4 Patch
U41 LohrPatterson2017 CRF Tavenier Nursery
U41 Lohr2020 U4 Patch
U41 Lohr2020 U14 Patch
U44 LohrPatterson2017 CRF Tavenier Nursery
U44 Lohr2020 U4 Patch
U47 LohrPatterson2017 CRF Tavenier Nursery
U73 LohrPatterson2017 CRF Tavenier Nursery
U77 LohrPatterson2017 CRF Tavenier Nursery
U77 Lohr2020 U4 Patch
U77 Lohr2020 U14 Patch
U78 LohrPatterson2017 CRF Tavenier Nursery

This leads me to believe that the composite growth index is not sensitive to data comprised only of calcification or linear extension metrics, rather, the index is sensitive to evenness of sampling effort where a few high growth values in a single metric may skew the composite score. While this dampens the robustness of our index as it stands today, the index will become more robust over time with the inclusion of more datasets from the lab and field.

To support this conclusion, I am recalculating the composite growth index. However, for this index, the calcification data for Katie Lohr’s work is removed. This calcification data was obtained by collecting the buoyant weight of corals grown in a coral nursery and dominates the buoyant weight metrics as all other buoyant weight growth measured corals grown in a lab where growth rates are typically much less than that of a nursery. Thus, these genotypes will now only be classified as linear extension. I am then recreating the exact plot and tables from above on this data subset.
Comparison of the composite index as a function of the classified type. Both denotes linear extension and calcification metrics are represented in the composite index. Calcification data from Lohr (2017) has been removed.
contrast estimate conf.low conf.high adj.p.value
G-Both -0.106 -0.634 0.422 0.882
LE-Both -0.030 -0.296 0.236 0.960
LE-G 0.076 -0.402 0.554 0.925

We can then compare the new index rankings with the old index rankings after the removal of Lohr (2017). We can see these few data points heavily weighed these genotypes.

Comparison of the composite index before and after filtering Lohr (2017).
genotype score.old metrics.old type.old score.new metrics.new type.new
U73 1.658 5 Both 1.027 3 LE
U47 1.587 5 Both 0.982 3 LE
K2 1.536 7 Both 0.229 5 LE
K3 1.530 7 Both 0.269 5 LE
U78 1.515 5 Both 0.836 3 LE
U41 1.455 7 Both 0.528 5 LE
U77 1.210 7 Both 0.435 5 LE
K1 1.072 5 Both 0.382 5 Both
U44 0.765 7 Both 0.195 5 LE

In conclusion, I believe the composite growth index can align the datasets and metrics within AcDC to best describe relative performance. While the index is not without its flaws, the robustness will only increase over time with the inclusion of more traits and datasets. By using the temporal, experimental, and location filters, one can further increase the robustness of the index. For instance, one can remove lab or field data using the filters to achieve the filtering of the Lohr (2017) calcification data.

Standardized Metric

To compare these rankings to individually derived metrics, please check out the other report.